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A152267 a(n) = ((9 + sqrt(8))^n + (9 - sqrt(8))^n)/2.

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%I A152267 #13 Sep 08 2022 08:45:39
%S A152267 1,9,89,945,10513,120249,1397033,16368417,192648097,2272771305,
%T A152267 26846572409,317325998097,3752068179889,44372429376921,
%U A152267 524802751652681,6207262185233025,73420118463548737,868431992821866441
%N A152267 a(n) = ((9 + sqrt(8))^n + (9 - sqrt(8))^n)/2.
%C A152267 Binomial transform of A145303. - _Philippe Deléham_, Dec 03 2008
%H A152267 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -73).
%F A152267 From _Philippe Deléham_, Dec 03 2008: (Start)
%F A152267 a(n) = 18*a(n-1) - 73*a(n-2), n > 1; a(0)=1, a(1)=9.
%F A152267 G.f.: (1-9*x)/(1-18*x+73*x^2).
%F A152267 a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*8^(n-k). (End)
%t A152267 LinearRecurrence[{18,-73},{1,9},30] (* _Harvey P. Dale_, May 14 2014 *)
%o A152267 (Magma) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((9+r8)^n+(9-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008
%K A152267 nonn
%O A152267 0,2
%A A152267 Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008
%E A152267 Extended beyond a(6) by _Klaus Brockhaus_, Dec 03 2008